Non-linear classification of finite-dimensional simple $C^*$-algebras
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909275043921920 |
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| author | Kuzma, Bojan Singla, Sushil |
| author_facet | Kuzma, Bojan Singla, Sushil |
| contents | A Banach space characterization of simple real or complex $C^*$-algebras is given which even characterizes the underlying field. As an application, it is shown that if $\mathfrak A_1$ and $\mathfrak A_2$ are Birkhoff-James isomorphic simple $C^*$-algebras over the fields $\mathbb F_1$ and $\mathbb F_2$, respectively and if $\mathfrak A_1$ is finite-dimensional with dimension greater than one, then $\mathbb F_1=\mathbb F_2$ and $\mathfrak A_1$ and $\mathfrak A_2$ are (isometrically) $\ast$-isomorphic $C^*$-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21582 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-linear classification of finite-dimensional simple $C^*$-algebras Kuzma, Bojan Singla, Sushil Operator Algebras Functional Analysis 46L05, 46B20, 46B80 A Banach space characterization of simple real or complex $C^*$-algebras is given which even characterizes the underlying field. As an application, it is shown that if $\mathfrak A_1$ and $\mathfrak A_2$ are Birkhoff-James isomorphic simple $C^*$-algebras over the fields $\mathbb F_1$ and $\mathbb F_2$, respectively and if $\mathfrak A_1$ is finite-dimensional with dimension greater than one, then $\mathbb F_1=\mathbb F_2$ and $\mathfrak A_1$ and $\mathfrak A_2$ are (isometrically) $\ast$-isomorphic $C^*$-algebras. |
| title | Non-linear classification of finite-dimensional simple $C^*$-algebras |
| topic | Operator Algebras Functional Analysis 46L05, 46B20, 46B80 |
| url | https://arxiv.org/abs/2407.21582 |